Crash Beliefs From Investor Surveys William N. Goetzmann Dasol Kim Robert J. Shiller Yale School of Management, Yale University Weatherhead School of Management, Case Western Reserve University Yale University Draft: March 5, 2016 PRELIMINARY Please do not quote without permission Abstract: Historical data suggest that the base rate for a severe, single-day stock market crash is relatively low. Surveys of individual and institutional investors, conducted regularly over a 26 year period in the United States with individual and institutional investors show that they assess the probability to be much higher. We examine the factors that influence investor response and test the role of media influence. We find evidence consistent with an availability bias. Recent market declines and adverse market events made salient by the financial press are associated with higher subjective crash probabilities. Non-market-related, rare disasters are also associated with higher subjective crash probabilities. JEL: G00, G11, G23, E03, G02 Acknowledgements: We thank the International Center for Finance at the Yale School of Management for support with the survey data. We thank Leigh Ann Clark, Sumithra Sudhir and Minhua Wan for help with the data. We thank Alan Moreira and Tyler Muir for their suggestions. The authors take responsibility for all errors. Please direct correspondence to: [email protected]
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Crash Beliefs From Investor Surveys
William N. Goetzmann
Dasol Kim
Robert J. Shiller
Yale School of Management, Yale
University
Weatherhead School of
Management, Case Western
Reserve University
Yale University
Draft: March 5, 2016
PRELIMINARY
Please do not quote without permission
Abstract: Historical data suggest that the base rate for a severe, single-day
stock market crash is relatively low. Surveys of individual and institutional
investors, conducted regularly over a 26 year period in the United States
with individual and institutional investors show that they assess the
probability to be much higher. We examine the factors that influence
investor response and test the role of media influence. We find evidence
consistent with an availability bias. Recent market declines and adverse
market events made salient by the financial press are associated with
Disaster risk and concerns about severe stock market crashes are the subject of considerable recent research.
Rare disaster concerns are relevant to the equity premium puzzle,1 time-varying market premiums2, cross-
sectional differences in asset returns3 the volatility smile4 and investor choice.5 Despite their potential
importance, rare disaster concerns are difficult to empirically quantify. Probabilities about extreme events
are usually inferred from asset prices, and disentangling probabilities from risk preferences presents
problems.6
In this paper, we turn to a different source of information about rare crash probabilities. Since 1989, Robert
Shiller has been surveying individual and institutional investors. One question in the Shiller survey asks
respondents to estimate the probability that a severe crash will occur over the next six months. The
definition of a crash is specific: a drop in the U.S. stock market on the scale of October 19th, 1987 [ -22.61%]
or October 28th 1929 [-12.82%]. This definition is particularly relevant to the jump tail risk literature.
Bollerslev and Todorov (2011) and Bollerslev, Todorov and Xu (2015) argue that a significant component
of priced tail risk is attributable to investor fears about a near-instantaneous crash similar to the one-day
drops of 1929 and 1987. A key question in this work and related literature is whether asset prices reflect
probabilities or preferences. As Ross (2015) puts it, “State prices are the product of risk aversion—the
pricing kernel—and the natural probability distribution.”
We use the Shiller survey data to examine the magnitude of crash probabilities reported by individual and
institutional investors. We find evidence that the average, subjective probability of an extreme, one-day
crash on the scale of 1987 or 1929 [i.e. greater than 12.82%] to be an order of magnitude larger than would
be implied by the historical frequency of such events in the U.S. market. Over the 1989-2015 period, the
mean and median probability assessments of a one-day crash were 19% and 10%, respectively. To the
extent that this rare crash risk fear is priced, our analysis suggests that it may function through extreme
probability assessments rather than through risk aversion.
We find that crash probabilities vary significantly through time and are correlated to measures of jump risk
such as the VIX and the occurrence of extreme negative returns. We also test behavioral hypotheses about
whether investor priors are subject to the influence of the media.
1 Cf. Reitz (1988), Barro (2006), Berkman et. al. (2011) and Welch (2015), Santa –Clara and Yan (2010). 2 Cf. Gabaix (2008), Wachter (2013), Tsai and Wachter (2015) and Manela and Moreira (2016). 3 Cf. Gao and Song (2015) 4 Cf. Bollerslev and Todorov (2011), Bates (2000) 5 Cf. Guerrero et.al (2015). 6 Cf. Jackwerth et. al. (1996), Seo and Wachter (2013) and Ross (2015).
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In particular, we test for the incremental effects of positive vs. negative crash-related terms about the market
on the days prior to the survey. We find evidence that the financial press mediates investor crash beliefs
asymmetrically. Articles with “crash” related terms are associated with higher crash probability
assessments, but articles with “boom” related terms are not. We test the hypothesis that this association
operates through the availability heuristic.
The availability heuristic (cf. Tversky and Kahneman, 1973 & Kahneman and Tversky (1982) is the
tendency to use easily recalled events to estimate the probability of an event occurring. Subjects prone to
the availability heuristic “bias” their probability beliefs by giving more weight to “top-of-mind” data.
Tversky and Kahneman (1973) tests show that it is possible to induce this bias through priming or framing.
Studies of the availability heuristic have mostly focused on stock price reactions to information. Akhtar et.
al. (2013) document an asymmetric response of stock prices to the release of consumer sentiment news.
They report evidence consistent with the availability heuristic – inferring shifts in probability assessment
from asset price changes. Kliger and Kudryavtsev (2010) likewise rely on the asymmetry implied by
negativity bias to test the availability heuristic. They find that stock price reactions to analyst upgrades are
weaker on days of large market moves. Taking a different tack, Nofsinger and Varma (2013) use investor
decisions to test for the availability bias. They argue that the investor tendency to repurchase a stock
previously held is evidence of reliance on the availability heuristic. The contribution of our study to
research on the availability heuristic in finance is that we directly test its relationship to probability
estimates; the setting in which the hypothesis was originally formulated by Tversky and Kahneman (1973).
The availability heuristic is particularly pertinent to investment decision-making because probability
assessment of events – for example, the likelihood of tail risk events, affects investor allocations to risky
assets.7 If investors give too much weight to recent market events – perhaps because they look at recent
investment outcomes– this may cause them to incorrectly estimate the probability of a crash. By the same
token, the media may frame recent events through selective reporting – emphasizing negative outcomes
and thus making them more available when a subject is asked to assess the probabilities of a related event.
We find evidence that investors use recent market performance to estimate probabilities about a crash. We
also find that the press makes negative market returns relatively more salient and this is associated with
individual investor probability assessments of a crash. This latter mechanism is consistent with Barber and
Odean (2008), Engelberg and Parsons (2011), Kräussl and Mirgorodskaya (2014),Yuan (2015) and other
research documenting evidence that the news plays an important role in focusing investor attention and
influencing behavior. Finally, we also find evidence consistent with an availability bias when examining
7 Cf. Barberis (2013).
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the crash probabilities of investors who recently experienced exogenous rare events; in this case, moderate
earthquakes.
The balance of the paper is organized as follows. Section 2 describes the data used in the analysis. Section
3 presents the empirical findings and a number of robustness tests. Section 4 concludes.
2. Data
2.1. Survey Data
Robert Shiller’s Stock Market Confidence Indices are based on survey data collected continuously since
1989; semi-annually for a decade and then monthly by the International Center for Finance at the Yale
School of Management since July, 2001. Shiller (2000) describes the indexes constructed from these
surveys and compares them to other sentiment indicators and studies their dynamics in the aggregate. In
this paper we use the disaggregated survey responses that are used to construct the indexes. About 300
questionnaires each month are mailed to individuals identified by a market survey firm as high-net-worth
investors and institutional investors. They may fill it in when they wish, but they are asked to mark the date
on which they complete the survey. It is not longitudinal survey – each month comprises a different sample
of respondents with the sampling goal of 20 to 50 responses by each of the two types – individual &
institutional. There is existing research that uses data from the Shiller surveys. Greenwood and Shleifer
(2015) find that the Shiller monthly investor confidence index is well-correlated to several other investor
surveys and to mutual fund flows. Goetzmann et. al. (2014) use the institutional investor responses from
a telephone version of the survey about beliefs in market mispricing in order to study variation in investor
mood. Their results are consistent with evidence derived from a different dataset of investor trading
behavior.
In the current study, we use responses to to the survey question:
“What do you think is the probability of a catastrophic stock market
crash in the U. S., like that of October 28, 1929 or October 19, 1987, in
the next six months, including the case that a crash occurred in the other
countries and spreads to the U. S.? (An answer of 0% means that it
cannot happen, an answer of 100% means it is sure to happen.)
Probability in U. S.:_______________%”
This question has been asked unaltered since the first survey was conducted. Thus it has the advantage of
consistency throughout a period of 26 years, during which time the stock market, the macro-economy and
the financial system has experienced considerable variation. In addition to the responses to the questions,
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survey participants provided the date on which the questionnaire was completed. Information about the ZIP
codes of the respondents is readily available from 2007. The combined sample contains 9,953 responses.
One issue of potential concern is that the phrasing of the question may make a crash salient and lead to a
heightened probability assessment. A more neutral question might have left out the term “catastrophic”
and the two crash dates, and instead asked the probability of a single day crash greater than 12% or 20%.
In other words, the phrasing itself might contribute to an availability bias. There are several other questions
in the Shiller surveys – some with positive and some with negative valence; all about the stock market.
These may also prime an investor response. These stimuli make it potentially difficult to identify the
marginal influence of news articles on probability assessments. However, if the high reported probabilities
were due solely to factors within the questionnaire, this would suggest that direct priming may be a source
of extreme availability bias about the market – an interesting fact in itself.
Figure 1 graphs the average annual probabilities for the individual and institutional respondents. It also
shows a set of additional variables: the annualized volatility of the daily DJIA, the largest negative return
in each year (represented as a positive number on the figure) and the VIX implied volatility. The individual
and institutional means are relatively similar. Crash probabilities were higher in the period 1997-2003 and
2007-2011. These periods also correspond to higher realized volatility, implied volatility and most extreme
one-day DJIA percentage declines. These trends suggest that the probability assessments change with
factors associated with extreme market declines. Not shown in the figure are probabilities inferred from
historical market performance. It is well known that a log-normal model is not appropriate to estimate the
probability of an extreme decline. The average daily standard deviation of the DJIA is about 1% and the
two crashes of interest are 12 times and 20 times the daily standard deviation. This has motivated the use
of mixed jump processes to describe stock market moves.8
A simple approach to estimating a baseline probability is to use the historical frequency of such events.
Under the assumption of an i.i.d. distribution of daily returns, and using the number of trading days since
October 23, 1929 through December 31, 1988 [taking the most conservative bounds] gives an average
probability of an extreme crash over a six-month horizon of 1.7%. This declines to about 1% when the
entire history of the DJIA is used. The average reported crash probability from the Shiller surveys is thus
more than 10 times the conservative estimate. Of course, it is possible that selection or survivorship has
biased the empirical estimate downwards. However, the frequency of a major one-day crash would need
to be ten times that observed in the US data, and have resulted in non-survival in order to arrive at a
8 Cf. Gabaix (2008), Wachter (2013), Bollerslev and Todorov (2011).
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conditional sample whose unconditional probability of a crash is consistent with the subjective probability
estimates in the Shiller survey.
2.2. Market Data
For stock market data, we use the daily Dow Jones Industrial Average, the S&P 500 and a value-weighted
index of the NYSE-AMEX-Nasdaq-Arca universe. We use returns of the DJIA to empirically measure
market volatility and the occurrence of extreme events. We also use the DJIA and the returns to the other
indexes on and before the day that the questionnaires are completed as a control for market trends that
jointly influence media articles and investor heuristics. Market volatility implied by the VIX is obtained
from FRED.
2.3. Media Data
We used ProQuest to search the Eastern Edition of the Wall Street Journal [WSJ] for the period of the
questionnaire sample: 1989-2015. This is the only edition available on ProQuest for that period. We
presume that it corresponds reasonably well to the national edition. Data were collected in the weeks of
January 24 & 31 of 2016. We searched articles containing words and phrases associated with a stock market
boom or a stock market crash.
The terms “stock market boom” and “stock market crash” came into widespread use in American English
in the 1920’s. Before 1924 there were virtually no instances of these terms in the Google Ngram corpus of
books published in America. This coincides closely with the emergence of widespread stock market
investing in the United States. The frequency of the use of both terms rose rapidly from 1929 to a local
peak in 1933, doubtless due to the crash of 1929. Their frequencies were more or less stable until the1987-
1990 period when the use of the term “stock market crash” more than doubled in frequency and then
declined – with some variation – until 2008, which is the terminal date for the corpus. 2003-2004 saw a
local maximum for the term “stock market boom” but the average ratio of the two terms is about 7:1 – with
“stock market crash” the more prevalent. While there are potential synonyms for “crash” and “boom”, and
constructing a variable through topic modeling or other latent semantic extraction techniques has potential,
our approach in this paper is to focus on the term “crash” and what we take to be its logical antonym. We
also augment the crash/boom pairing with more general positive and negative terms such as “good/bad”
and “good news” bad news.” These terms are less specific descriptors of the market and are more moderate
in valence, but they increase our sample size.
Because of the potential for data-snooping, all searches are listed in Table 1, and the terms we use for
analysis are identified. Although some of the terms in the table are only tangentially related to the current
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study, we have retained them for completeness. In certain cases, we searched on a term like “market crash”
and then discovered that many articles were about other kinds of markets. We then re-ran the search with
the added term “stock market” but retained the unconditional results for completeness. In addition, we
intended to test some predictions about the relation between negative events and causality. Although not
the topic of this study, we include these for completeness.
Garcia (2014) documents a significant asymmetry in media reportage of past market returns – negative
outcomes are reported more frequently in certain Wall Street Journal columns. This is consistent with
evidence that both animals and humans are conditioned to give stronger weight to negative things,
experiences and events (cf. Baumeister et. al., 2001 and Rozin and Royzman, 2001). Negative experiences
engage greater cognitive effort (Ito et. al., 1998), have greater influence in evaluations (Ito et. al., 1998),
are more likely to be taken as valid (Hilbig, 2009) increase arousal, and enhance the memory and
comprehension of the event (Grabe and Kammhawi, 2006). These prior results lead us to expect that (1)
negative news is more prevalent in our sample of crash and boom related terms, and (2) the availability bias
– if it exists – should be asymmetric. Negative events and terms should have a greater effect on probability
assessments than positive events and terms.
Table 1 summarizes the results of the ProQuest search. Of some interest is the higher number of articles
containing the words “good news” [15,372] as opposed to “bad news” [10,751]. This contrasts to the
presumption that the news generally has a negativity bias. However, when we condition on the additional
term “stock market,” this ratio decreases [2,342 versus 2,182] and is not statistically significantly different
from the fraction of positive DJIA days [52%].
3. Empirical Results
3.1. Summary Statistics
Table 2 displays the variable descriptions and summary statistics. The interquartile range of the stock
indices are comparable, through the overall range for the NYSE-AMEX-Nasdaq-Arca and S&P 500 indices
are slightly larger than that of the DJIA index. The mean and median of the subjective probabilities are
reported. They are 19% and 19% respectively indicating a positive skew.
3.2. Media Responses to Market Events
We begin by examining the relationship between returns and the valence and subject matter of WSJ articles
on the following day. As a preview of the results, we show that negative returns in the prior day(s) are
associated with significantly higher negative article counts, and positive returns are associated with
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significantly higher positive article counts, although the positive results are somewhat weaker.9 There are
significant coefficients on volatility, signed extreme returns, prior month returns, and positive/negative